NAME

math_error - detecting errors from mathematical functions

SYNOPSIS

#include<math.h>#include<errno.h>#include<fenv.h>

DESCRIPTION

When an error occurs, most library functions indicate this fact by
returning a special value (e.g., -1 or NULL). Because they typically
return a floating-point number, the mathematical functions declared in
<math.h> indicate an error using other mechanisms. There are two
error-reporting mechanisms: the older one sets errno; the newer one
uses the floating-point exception mechanism (the use of
feclearexcept(3) and fetestexcept(3), as outlined below) described in
fenv(3).
A portable program that needs to check for an error from a mathematical
function should set errno to zero, and make the following call
feclearexcept(FE_ALL_EXCEPT);
before calling a mathematical function.
Upon return from the mathematical function, if errno is nonzero, or the
following call (see fenv(3)) returns nonzero
fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW |
FE_UNDERFLOW);
then an error occurred in the mathematical function.
The error conditions that can occur for mathematical functions are
described below.
DomainError
A domainerror occurs when a mathematical function is supplied with an
argument whose value falls outside the domain for which the function is
defined (e.g., giving a negative argument to log(3)). When a domain
error occurs, math functions commonly return a NaN (though some
functions return a different value in this case); errno is set to EDOM,
and an "invalid" (FE_INVALID) floating-point exception is raised.
PoleError
A poleerror occurs when the mathematical result of a function is an
exact infinity (e.g., the logarithm of 0 is negative infinity). When a
pole error occurs, the function returns the (signed) value HUGE_VAL,
HUGE_VALF, or HUGE_VALL, depending on whether the function result type
is double, float, or longdouble. The sign of the result is that which
is mathematically correct for the function. errno is set to ERANGE,
and a "divide-by-zero" (FE_DIVBYZERO) floating-point exception is
raised.
RangeError
A rangeerror occurs when the magnitude of the function result means
that it cannot be represented in the result type of the function. The
return value of the function depends on whether the range error was an
overflow or an underflow.
A floating result overflows if the result is finite, but is too large
to represented in the result type. When an overflow occurs, the
function returns the value HUGE_VAL, HUGE_VALF, or HUGE_VALL, depending
on whether the function result type is double, float, or longdouble.
errno is set to ERANGE, and an "overflow" (FE_OVERFLOW) floating-point
exception is raised.
A floating result underflows if the result is too small to be
represented in the result type. If an underflow occurs, a mathematical
function typically returns 0.0 (C99 says a function shall return "an
implementation-defined value whose magnitude is no greater than the
smallest normalized positive number in the specified type"). errno may
be set to ERANGE, and an "overflow" (FE_UNDERFLOW) floating-point
exception may be raised.
Some functions deliver a range error if the supplied argument value, or
the correct function result, would be subnormal. A subnormal value is
one that is nonzero, but with a magnitude that is so small that it
can’t be presented in normalized form (i.e., with a 1 in the most
significant bit of the significand). The representation of a subnormal
number will contain one or more leading zeros in the significand.

NOTES

The math_errhandling identifier specified by C99 and POSIX.1-2001 is
not supported by glibc. This identifier is supposed to indicate which
of the two error-notification mechanisms (errno, exceptions retrievable
via fettestexcept(3)) is in use. The standards require that at least
one be in use, but permit both to be available. The current (version
2.8) situation under glibc is messy. Most (but not all) functions
raise exceptions on errors. Some also set errno. A few functions set
errno, but don’t raise an exception. A very few functions do neither.
See the individual manual pages for details.
To avoid the complexities of using errno and fetestexcept(3) for error
checking, it is often advised that one should instead check for bad
argument values before each call. For example, the following code
ensures that log(3)’s argument is not a NaN and is not zero (a pole
error) or less than zero (a domain error):
double x, r;
if (isnan(x) || islessequal(x, 0)) {
/* Deal with NaN / pole error / domain error */
}
r = log(x);
The discussion on this page does not apply to the complex mathematical
functions (i.e., those declared by <complex.h>), which in general are
not required to return errors by C99 and POSIX.1-2001.
The gcc(1) -fno-math-errno option causes the executable to employ
implementations of some mathematical functions that are faster than the
standard implementations, but do not set errno on error. (The gcc(1)
-ffast-math option also enables -fno-math-errno.) An error can still
be tested for using fetestexcept(3).